Schulmann, Viktor2021-06-072021-06-072021-03-01http://hdl.handle.net/2003/4024010.17877/DE290R-22113Let X=(Xt)t≥0 be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of XT. Belomestny and Schoenmakers (Stoch Process Appl 126(7):2092–2122, 2015) propose a solution based the Mellin transform in case where X is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of T for a self-similar one-dimensional process X. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.enStatistical inference for stochastic processes;24https://creativecommons.org/licenses/by/4.0/Estimation of stopping timesMultiplicative deconvolutionMellin transformSelf-similar processBessel process510article (journal)